1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zheka24 [161]
2 years ago
15

Please show work and thank youuu

Mathematics
1 answer:
Assoli18 [71]2 years ago
3 0

Answer:  6\sqrt{3}

======================================================

Explanation:

Method 1

We can use the pythagorean theorem to find x.

a^2+b^2 = c^2\\\\6^2+x^2 = 12^2\\\\36+x^2 = 144\\\\x^2 = 144-36\\\\x^2 = 108\\\\x = \sqrt{108}\\\\x = \sqrt{36*3}\\\\x = \sqrt{36}*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 2

Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2

\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(60^{\circ}) = \frac{x}{12}\\\\\frac{\sqrt{3}}{2} = \frac{x}{12}\\\\x = 12*\frac{\sqrt{3}}{2}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 3

Similar to the previous method, but we'll use tangent this time.

Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)

\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(60^{\circ}) = \frac{x}{6}\\\\\sqrt{3} = \frac{x}{6}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 4

This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.

Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.

\text{long leg} = (\text{short leg})*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

The short leg is always opposite the smallest angle (30 degrees).

You might be interested in
Suppose a model airplane club publishes a newsletter. Expenses are $0.90 for printing and mailing each copy, plus $600 total for
Oduvanchick [21]
They would have to sell around a 1000 newspapers

7 0
3 years ago
Purple Dog Pet Supply Inc. (PDPS) released its annual results and financial statements. Lucia is reading the summary in the busi
Rama09 [41]

Answer:

$35,000

Step-by-step explanation:

The computation of the dividend amount is given below:

As we know that

Dividend Paid = Net income - Retained earnings for current year

where,

Retained earnings for current year = This year - last year

= $500,000 - $425,000

= $75,000

Now

Dividend Paid is  

= $110,000 - $75,000

= $35,000

4 0
2 years ago
A bakery offers a sale price of $3.30 for 3 muffins. What is the price per dozen?
hram777 [196]

Answer:

The price for 12 muffins is $10.00

5 0
3 years ago
The sum of the first four terms of an arithmetic sequence is $10$. If the fifth term is $5$, what is the sixth term?
Nookie1986 [14]

The sixth term of an arithmetic sequence is 6

<h3>How to find arithmetic sequence?</h3>

The sum of the first four terms of an arithmetic sequence is 10.

The fifth term is 5.

Therefore,

sum of term = n / 2(2a + (n - 1)d)

where

  • a = first term
  • d = common difference
  • n = number of terms

Therefore,

n = 4

10 = 4 / 2 (2a + 3d)

10 = 2(2a + 3d)

10 = 4a + 6d

4a + 6d = 10

a + 4d = 5

4a + 6d = 10

4a + 16d = 20

10d = 10

d = 1

a + 4(1) = 5

a = 1

Therefore,

6th term = a + 5d

6th term = 1 + 5(1)

6th term = 6

learn more on sequence here: brainly.com/question/24128922

#SPJ1

7 0
1 year ago
What statement about a rhombus is always true?
Harlamova29_29 [7]
I'm going to say A and B
6 0
3 years ago
Read 2 more answers
Other questions:
  • How do i solve x/3+1=3
    11·2 answers
  • The first three terms of an arithmetic sequence are as follows
    9·1 answer
  • The height of an ostrich is 20 inches more than 4 times the height of a kiwi. Write and solve an equation to find the height of
    8·1 answer
  • Which pair of numbers are relatively prime
    9·2 answers
  • Subtract.
    6·1 answer
  • Winston earns $140.00 by selling 56 hot dogs at a concession stand at school. Using the same rate for the cost of one hot dog, h
    8·1 answer
  • The price of a watch was increased by 20% to £162. <br> What was the price before the increase?
    12·1 answer
  • What is the slope of the line
    11·1 answer
  • Find the amount owed:<br> $12,460 loan at 5.6% interest for 30 months
    9·1 answer
  • OMG GUYS HELP ME I GIVE 100 points what is 1+1 and what is 2-1 tell me!!! QUICK
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!